Specific heat Schottky anomaly

In metallic compounds, optical methods cannot be used to determine the crystal-field levels. The determination of crystal field levels in such compounds has been reviewed by Fulde (1979) and is only mentioned here. These are primarily based on measurements of the magnetic susceptibility, magnetization in high magnetic field, specific heat (Schottky anomaly), Mossbauer effect, electron paramagnetic resonance, and inelastic neutron scattering. 

An example of magnetic contributions to the specific heat is reported in Fig. 3.9 that shows the specific heat of FeCl24H20, drawn from data of ref. [35,36]. Here the Schottky anomaly, having its maximum at 3K, could be clearly resolved from the lattice specific heat as well as from the sharp peak at 1K, which is due to a transition to antiferromagnetic order (lambda peak). 

Schottky anomaly is determined from the difference between an RY compound and LaX or LuX compound. Then the crystal field parameters are deduced from the Schottky anomaly data. The accuracy of the method is limited by spin-phonon interactions and exchange effects in rare earth ions which affect the Schottky effect, ft is used to find crystal field parameters, W, x which fit the specific heat data as shown in Fig. 8.4. The figure refers to a plot of C/Rq vs. T for TmAF [19]. 

The cluster compounds [Ag6M4Pi2]Gc6 with = Ge, Sn show at low temperatures a valence fluctuation of the inner core Ag6" +, which can be seen in the elastic behavior " and vibrational anharmonicity as well as in the measurements of the specific heat. The valence fluctuations generate a pronounced schottky anomaly, which can be emphasized more clearly by the comparison and therefore possible normalisation of cluster compounds. 

The Schottky-like anomaly observed in the specific heat of the compounds discussed in this section can be derived phenomenologically using (a) the resonance-level model, (b) the spin glass behaviour, (c) the crystal field (Schottky) contribution or even (d) low-dimensional magnetic fluctuations. The cases where an HF behaviour is deduced from a large value will be discussed in sect. 9, in connection with the contribution to of the excited crystal field levels. It is clear that complementary techniques, such as NMR, AC susceptibility and electrical resistivity, can easily reveal the magnetic character of the microscopic interactions. In some of the HF compounds the ratio between the y term and the (( -> 0) = Xo value of the susceptibility, and between the / term and the coefficient of the resistivity. A, have values predicted by... 

Fig. 26. High-temperature specific heat of three Kondo eompounds with an abnormal Schottky anomaly, after de Boer et al. (1985) and Felten (1987). The continuous curve is a Schottky contribution for a F-j-Fg thermal promotion.

Fig. 16. Temperature dependence of 4f-derived specific heat, C, and entropy in units of the gas constant, SJR, for (a) CeRu j Gcj and (b) CeCu GCj (Felten et al. 1987). Solid curves in upper parts show Schottky anomalies corresponding to the CF splitting of Ce given in the text.

Fig. 69. The 5f-derived specific heat of URUjSij, AC, as a function of temperature (on a logarithmic scale) (Renker et al. 1987b). Thick line shows Schottky anomaly for doublet-doublet CF system with a sphtting of kg 75 K. Thin line is guide to the eye.

THE SCHOTTKY-TYPE ANOMALY IN THE SPECIFIC HEAT OF SOLID CH3D. 

U. Kohler, R. Demchyna, S. Paschen, U. Schwarz, F. Steglich, Schottky anomaly in the low-temperature specific heat of Bag.j,EUj,Ge43n3. Physica B 378-380, 263 (2006)... 

Fig. 63. Left panel Complete B-T phase diagram (Maple et al., 2002) with SC regime and region of field induced order parameter which is presumably of antiferroquadrupolar (AFQ) type. Data are obtained from resistivity (p), magnetization (M), specific heat (C) and thermal expansion (o ) measurements. Right panel High magnetic field phase diagram (Aoki et al., 2003) with upper part of AFQ phase (full squares) and line of high field Schottky anomaly from the Fi-Fs crossing. The inset shows calculation for tetrahedral CEF model.

As can be seen in the article by de Jongh and Miedema (1974) the specific-heat anomalies of low-dimensional systems are similar to Schottky peaks. The same is true for systems which have only short-range magnetic interactions. 

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